What are some of your tips and tricks for running a fun/competitive team?
One thing to keep in mind is that not everyone on your team could have the same objectives. I see a lot of good advice here for very competitive teams, but it's quite possible you'll have a much more "social" lineup.
What technology are you using to help manage your team? (Chat, rosters, social stuff, etc)
I'd second the concern with only using text/email. I've been amazed how hard it can be to get people to respond/read a text. That's assuming your phone carriers don't mess up the delivery, which isn't uncommon when you have "large" group chats across providers and devices (iPhone & Android). If you do go this route I would encourage you to individually message people when you expect them to show up and always request a confirmation back.
How do you go about assigning match lanes?
I'm going to assume you don't know everyone well. I would recommend you try out different doubles pairings early to try and figure out who works well together and against their opponents. It'll also give them a chance to gain a feel for each other's games. For both singles & doubles, you'll want to figure out, as Cindy says, if people have difficulty on different positions (whether it's mental or physical).
Don't be fooled by flashy hitters in practice. Lots of "big hitters" at 4.0 shrink under pressure in a match, and you might be better off with that steady, smart player who can control their shots (especially in singles).
Do you hold weekly (optional or not) practices?
Unless this is a team you assembled with a particular goal in mind and everyone bought into that, I certainly wouldn't try to have "mandatory" practices. I suggest that you try to facilitate opportunities for voluntary practices*. It's unlikely you will get everyone together for the same day twice a week, so it might be that you guys have two nights for different groups.
*By practice I don't exclusively mean "drilling". Sure, it's the best way to improve, but a lot of people just aren't going to make showing up for that a priority. You can still get good value out of playing situational tennis outside of "league play" where many people are consumed with winning versus improving. Then if someone is struggling with something (ex. overheads) you and them can go to another court and work on that technique specifically.
As far as "pro" lead practices, it wouldn't be my preference. I've always been somewhat skeptical of group practices led by pros anyway, at least in the sense that I'd prefer a small session (1-3 people). I'm not trying to change my whole game, so if I want extra help it's on very specific things, and that's best accomplished in the smaller group.
One other thing that can work well, if you've got the connections, is to bring in "better" players to hit with your guys. Sometimes the extra pace and talent can help expose mistakes that people are simply getting away with against inferior competition.
Some players do not want an unschooled peer telling them how to play.
This is very true. I don't offer much outside of support to teammates unless I'm sure they want it. Fortunately it's not usually hard to figure out who wants advice.
Finally, you're going to have to sacrifice playing time (both at practice and in matches) to try and observe people for much of this advice. Just looking at score results won't tell you enough about a player to understand why they won. That can be especially true in doubles where two good players just don't get along sometimes.
Good luck with your team in 2019!